International patent application WO 00/31420 discloses a pressure medium accumulator of this general type. Movement of the pleated bellows causes the closing member of the bottom valve to adopt a position where it carries out the function of a hydraulic piston. The reliability of operation is considerably enhanced because this arrangement reliably prevents damage to the bottom valve and an inadvertent escape of pressure medium. However, the above-mentioned publication does not provide any way for reliably filling the chambers referred to above without damaging the pleated bellows.